%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG030+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 06:49:12 AM UTC 2026
% Result : Theorem 0.16s 5.41s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 32 ( 19 unt; 0 def)
% Number of atoms : 75 ( 32 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 61 ( 18 ~; 9 |; 12 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn 20 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax3,axiom,
~ ! [U] :
( sorti1(U)
=> ! [V] :
( sorti1(V)
=> op1(U,V) = op1(V,U) ) ),
file('theBenchmark.p',ax3) ).
fof(ax4,axiom,
~ ~ ! [U] :
( sorti2(U)
=> ! [V] :
( sorti2(V)
=> op2(U,V) = op2(V,U) ) ),
file('theBenchmark.p',ax4) ).
fof(co1,conjecture,
( ( ! [V] :
( sorti2(V)
=> sorti1(j(V)) )
& ! [U] :
( sorti1(U)
=> sorti2(h(U)) ) )
=> ~ ( ! [X2] :
( sorti1(X2)
=> j(h(X2)) = X2 )
& ! [X1] :
( sorti2(X1)
=> h(j(X1)) = X1 )
& ! [Y] :
( sorti2(Y)
=> ! [Z] :
( sorti2(Z)
=> j(op2(Y,Z)) = op1(j(Y),j(Z)) ) )
& ! [W] :
( sorti1(W)
=> ! [X] :
( sorti1(X)
=> h(op1(W,X)) = op2(h(W),h(X)) ) ) ) ),
file('theBenchmark.p',co1) ).
fof(co1_neg,negated_conjecture,
~ ( ( ! [V] :
( sorti2(V)
=> sorti1(j(V)) )
& ! [U] :
( sorti1(U)
=> sorti2(h(U)) ) )
=> ~ ( ! [X2] :
( sorti1(X2)
=> j(h(X2)) = X2 )
& ! [X1] :
( sorti2(X1)
=> h(j(X1)) = X1 )
& ! [Y] :
( sorti2(Y)
=> ! [Z] :
( sorti2(Z)
=> j(op2(Y,Z)) = op1(j(Y),j(Z)) ) )
& ! [W] :
( sorti1(W)
=> ! [X] :
( sorti1(X)
=> h(op1(W,X)) = op2(h(W),h(X)) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_3,plain,
? [U] :
( ? [V] :
( op1(V,U) != op1(U,V)
& sorti1(V) )
& sorti1(U) ),
inference(fof_nnf,[status(thm)],[ax3]) ).
fof(sk_ax3,plain,
( op1(sK1,sK0) != op1(sK0,sK1)
& sorti1(sK1)
& sorti1(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(U,sK0),skolemize(V,sK1)],[nnf_3]) ).
cnf(c_8,plain,
sorti1(sK0),
inference(split_conjunct,[status(thm)],[sk_ax3]) ).
cnf(c_9,plain,
sorti1(sK1),
inference(split_conjunct,[status(thm)],[sk_ax3]) ).
cnf(c_10,plain,
op1(sK1,sK0) != op1(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_ax3]) ).
cnf(c_11,plain,
( op2(B,A) = op2(A,B)
| ~ sorti2(B)
| ~ sorti2(A) ),
inference(clausify,[status(thm)],[ax4]) ).
cnf(c_12,negated_conjecture,
( sorti2(h(A))
| ~ sorti1(A) ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_15,negated_conjecture,
( j(op2(A,B)) = op1(j(A),j(B))
| ~ sorti2(B)
| ~ sorti2(A) ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_17,negated_conjecture,
( j(h(A)) = A
| ~ sorti1(A) ),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_22,negated_conjecture,
sorti2(h(sK1)),
inference(resolve,[status(thm)],[c_12,c_9]) ).
cnf(c_23,negated_conjecture,
sorti2(h(sK0)),
inference(resolve,[status(thm)],[c_12,c_8]) ).
cnf(c_28,negated_conjecture,
j(h(sK1)) = sK1,
inference(resolve,[status(thm)],[c_17,c_9]) ).
cnf(c_29,negated_conjecture,
j(h(sK0)) = sK0,
inference(resolve,[status(thm)],[c_17,c_8]) ).
cnf(c_50,negated_conjecture,
( j(op2(h(sK1),A)) = op1(j(h(sK1)),j(A))
| ~ sorti2(A) ),
inference(resolve,[status(thm)],[c_15,c_22]) ).
cnf(c_51,negated_conjecture,
j(op2(h(sK1),h(sK0))) = op1(j(h(sK1)),j(h(sK0))),
inference(resolve,[status(thm)],[c_50,c_23]) ).
cnf(c_52,negated_conjecture,
j(op2(h(sK1),h(sK0))) = op1(sK1,j(h(sK0))),
inference(paramod,[status(thm)],[c_28,c_51]) ).
cnf(c_44,negated_conjecture,
j(op2(h(sK1),h(sK0))) = op1(sK1,sK0),
inference(paramod,[status(thm)],[c_29,c_52]) ).
cnf(c_53,negated_conjecture,
( j(op2(h(sK0),A)) = op1(j(h(sK0)),j(A))
| ~ sorti2(A) ),
inference(resolve,[status(thm)],[c_15,c_23]) ).
cnf(c_54,negated_conjecture,
j(op2(h(sK0),h(sK1))) = op1(j(h(sK0)),j(h(sK1))),
inference(resolve,[status(thm)],[c_53,c_22]) ).
cnf(c_55,negated_conjecture,
j(op2(h(sK0),h(sK1))) = op1(sK0,j(h(sK1))),
inference(paramod,[status(thm)],[c_29,c_54]) ).
cnf(c_45,negated_conjecture,
j(op2(h(sK0),h(sK1))) = op1(sK0,sK1),
inference(paramod,[status(thm)],[c_28,c_55]) ).
cnf(c_56,plain,
( op2(A,h(sK1)) = op2(h(sK1),A)
| ~ sorti2(A) ),
inference(resolve,[status(thm)],[c_11,c_22]) ).
cnf(c_57,plain,
op2(h(sK0),h(sK1)) = op2(h(sK1),h(sK0)),
inference(resolve,[status(thm)],[c_56,c_23]) ).
cnf(c_46,plain,
op2(h(sK1),h(sK0)) = op2(h(sK0),h(sK1)),
inference(copy,[status(thm)],[c_57]) ).
cnf(c_58,negated_conjecture,
j(op2(h(sK0),h(sK1))) = op1(sK1,sK0),
inference(paramod,[status(thm)],[c_46,c_44]) ).
cnf(c_59,negated_conjecture,
op1(sK0,sK1) = op1(sK1,sK0),
inference(paramod,[status(thm)],[c_45,c_58]) ).
cnf(c_48,negated_conjecture,
op1(sK1,sK0) = op1(sK0,sK1),
inference(copy,[status(thm)],[c_59]) ).
cnf(c_49,plain,
$false,
inference(resolve,[status(thm)],[c_48,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG030+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.38 % Computer : n002.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Sat Sep 26 21:02:27 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.39 % Process 2693226 was started by sandbox on n002,
% 0.11/5.39 % Sat Sep 26 21:02:27 2026
% 0.11/5.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/5.39
% 0.11/5.39 % From the command line: assign(max_seconds, 300).
% 0.16/5.41
% 0.16/5.41 % SZS status Theorem for theBenchmark
% 0.16/5.41
% 0.16/5.41 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.16/5.41 % Length of proof is 19.
% 0.16/5.41 % Level of proof is 5.
% 0.16/5.41 % Maximum clause weight is 14.000.
% 0.16/5.41 % Given clauses 15.
% 0.16/5.41
% 0.16/5.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------